# Question:Equation of an ellpise after rotation

## Question:Equation of an ellpise after rotation

Maple 2021

restart:local D:
with(plots):
with(plottools):

a := 7;
b := a/2;
NULL;

r := b/2;
c := 2*sqrt(10)*r;
A := [c/2, c/2];
B := [c/2, -1/2*c];
C := [-c/2, (-c)/2];
D := [-c/2, c/2];
f := (x, y) -> x^2/a^2 + y^2/b^2 = 1;
Ell1 := rotate(implicitplot(f(x, y), x = -9 .. 9, y = -6 .. 6, color = blue), Pi/4);

g := (x, y) -> x^2/b^2 + y^2/a^2 = 1;
Ell2 := rotate(implicitplot(g(x, y), x = -10 .. 10, y = -10 .. 10, color = blue), Pi/4);

quadri := plot([A, B, C, D, A], x = -6 .. 6, y = -6 .. 6, filled = true, color = red, transparency = 0.7);
Cir1 := disk([c/2 - r, -c/2 + r], r, color = blue);
Cir2 := disk([-c/2 + r, -c/2 + r], r, color = blue);
Cir3 := disk([-c/2 + r, c/2 - r], r, color = blue);
Cir4 := disk([c/2 - r, c/2 - r], r, color = blue);
display([quadri, Ell1, Ell2, Cir1, Cir2, Cir3, Cir4], scaling = constrained, axes = normal);
how to find the equations of ellipses in order to fit them to discs and whiten the interior of ellipses ? Thank you.

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